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On quantum quadratic operators of 𝕄 2 () and their dynamics. (English) Zbl 1210.47081
The paper deals with the study of nonlinear dynamics of quantum quadratic operators (q.q.o.) acting on the algebra of (2×2)-matrices 𝕄 2 (). The authors describe q.q.o. with Haar state as well as quadratic operators with the Kadison-Schwarz property. Using that description, they provide an example of q.q.o. which is not the Kadison-Schwarz operator. Moreover, the stability of the dynamics of q.q.o. is also studied.
MSC:
47H60Multilinear and polynomial operators
46L30States of C * -algebras
81R15Operator algebra methods (quantum theory)
15A99Miscellaneous topics in linear algebra
46L60Applications of selfadjoint operator algebras to physics
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